Simplify the following expression: $ r = \dfrac{7}{4} + \dfrac{-3}{7q + 1} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7q + 1}{7q + 1}$ $ \dfrac{7}{4} \times \dfrac{7q + 1}{7q + 1} = \dfrac{49q + 7}{28q + 4} $ Multiply the second expression by $\dfrac{4}{4}$ $ \dfrac{-3}{7q + 1} \times \dfrac{4}{4} = \dfrac{-12}{28q + 4} $ Therefore $ r = \dfrac{49q + 7}{28q + 4} + \dfrac{-12}{28q + 4} $ Now the expressions have the same denominator we can simply add the numerators: $r = \dfrac{49q + 7 - 12}{28q + 4} $ $r = \dfrac{49q - 5}{28q + 4}$